I write the save to my SD card but then I load up on my flashcart and it doesn't load the save that was written, instead it writes like if it wasn't written. It doesn't load any moves or pokémon I modified.

Theory might work.
0. Backup your save
1. Completey delete the save file from the Pokemon game as in hit New game to see how
2. Now put in your new save.
3. If dne correctly, it might not, you should have the edited save.